How People React to a Deadline: The Distribution of Registrations of Statphys 23

In Fig. 1 we show the number of registrations to Statphys 23
(full dots).
Each point corresponds to one day and the deadline $T^*$=March 31 was
the one corresponding to the early registration and abstract submission.
We also plot the data corresponding to the a different conference
(EP2DS 17)
for which we have rescaled the total number of registration at its
own $T^*$.
The data of the two conferences are remarkably similar
and are characterized by an initial linear behavior followed
by a strong increase near $T^*$.
This strong similarity suggests for a simple mechanism to describe
the response of the people to a deadline and we propose have a
simple model.
The basic idea is that the pressure you have to register is proportional
to the inverse of the remaining time to the deadline.
This gives a probability, $p(t)$, to register at time $t$ that is $p(t)\propto
\frac 1(T^*-t)$.
From this the number of the registrations at time $t$ is:
$$
N(t)=Cınt_0^T^*p(t)\;dt=A(N_tot)\;łn(T^*T^*-t).
\nonumber
$$
The logarithmic singularity at the end is regularized by discretizing the
integral with an interval of one day and the constant $A(N_tot)$
is fixed by the total number of final registration $N_tot$.
As one can see in Fig. 1 this simple model fits the
observed behavior extremely well.
This permits to predict the total number of registrations
already from the initial slope.
A result that could have some practical interest.
The model only assumes that the probability to register
is the same for the whole interval of the the remaining time.
In this respect there is no real tendency to shift the registration
towards the deadline.
The increase of pressure is just due to the approaching of the deadline.
This situation may appear curious because one could have expected
a stronger pressure to postpone the payment towards the deadline.
In this respect, however, one should notice that the data in Fig. 1
refer only to the registration and not to the payment of the fee which
could have been done also at a late time.

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